ON A CLASS OF NONLINEAR ELLIPTIC EQUATIONS

On a Class of Nonlinear Elliptic Equations and Boundary Value Problems in the Limit Domain

Hoang Quoc Toan

Abstract

In this paper we study the boundary value problem for a class of high order nonlinear elliptic equations in the bounded domain G₀ with smooth boundary Γ₀ in the space Rⁿ , where the domain G₀ is considered as a limit (in some sense) of the family of domain G₀ which depend smoothly on a parameter t Î [0, T] in S. G. Krein's sense when t tends to 0.